In information theory [1]}, Gaussian distribution with mean \(\mu \)  and variance \(\sigma ^2\)  is denoted by \(\mathcal {N}(\mu , \sigma ^2)\) . Its probability density function is
\(\mathcal {N}(\mu ,\sigma ^2) = \frac{1}{\sqrt{2\pi \sigma ^2}}e^{-\frac{(x-\mu )^2}{2\sigma ^2}}\) 
